Question

I am looking for an easy way to generate a simple linear map in Octave. The matrix I need, call it sigma(n), is defined by the following property: for all matrices A and B (both of dimension n) we have the equation:
sigma(n) * kron(A,B) = kron(B,A) * sigma(n)

For example,
sigma(2) = [1,0,0,0; 0,0,1,0; 0,1,0,0; 0,0,0,1].

Is there a simple function for sigma(n)?

For my purposes n will be fairly small, less than 50, so efficiency is not a concern.

EDIT: now with the correct defining equation

Answer 1

I realise it’s bad form to answer one’s own question, but with a small amount of head scratching I managed to generate the matrix explicitly:

function sig = sigma_(n) 
  sig = zeros(n^2,n^2);
  for i = 0:(n-1)
    for j = 0:(n-1)
      sig(i*n + j + 1, i+ (j*n) + 1) = 1;
    endfor
  endfor
endfunction

If anyone has a neater way to do this, I’m still interested.